A 100-voter Condorcet election example

By Warren D. Smith, Feb. 2014

#voters

Their Vote

35

A>B>C

21

B>A>C

21

B>C>A

21

C>A>B

1

A>C>B

1

C>B>A

A is the Condorcet winner,
beating B pairwise by 57:43
and also
beating C pairwise by 57:43.
Now: one voter each of types "A>C>B," "B>A>C," and "C>B>A"
– as well as 21 voters each of the types "B>C>A," "C>A>B," and "A>B>C"
(which form a reversed-direction cycle) –
all together should constitute a three-way tie.
So those votes should cancel out.
If we remove those 66=21×3+3 "cancelled out" ballots,
then we get:

#voters

Their Vote

14

A>B>C

20

B>A>C

whereupon B becomes the Condorcet winner!
Namely, B beats A pairwise by 20:14,
and B also beats C pairwise by 34:0.
(And B is the IRV winner, and also Borda winner, in both elections.)

This seems to demonstrate a self-contradiction within the Condorcet philosophy.